Hiccup on looping lego walk cycle
As you already mentioned (Edit 2) the hiccup is caused by 2 (or more) frames that are very similar when you move the master bone. A solution might be to shorten the walk cycle by one frame as described here: How to create a seamless animation loop in Blender?
In addition, the motion of the body does not appear to be constant over time. In some frames, when the legs are apart, the body has a fast forward motion. While it barely moves forward when the other leg passes the standing leg. This creates that &quot;striding like at a wedding&quot; effect. Maybe you can fix it by re-arranging the keyframes/poses.

I am not an expert on animation but I think you can create an action for the walk cycle and repeat this action in the NLA editor. So you don't have to animate it over and over again. Have a look here:  How should an animated character be moved while repeating a walk cycle?